Signatures of complex optical response in Casimir interactions of type I and II Weyl semimetals

The Casimir interaction, induced by electromagnetic fluctuations between objects, is strongly dependent upon the electronic and optical properties of the materials making up the objects. Here we investigate this ubiquitous interaction between semi-infinite spaces of topologically nontrivial Weyl semimetals. A comprehensive examination of all components of the bulk conductivity tensor and the surface conductivity due to the Fermi arc states in real and imaginary frequency domains is presented using the Kubo formalism for materials with different degree of tilting of their linear energy cones. The Casimir energy is calculated using a generalized Lifshitz approach, for which electromagnetic boundary conditions for anisotropic materials were derived and used. We find that the interaction between Weyl semimetals is metallic-like and its magnitude and characteristic distance dependence can be modified by the degree of tilting and chemical potential. The nontrivial topology plays a secondary role in the interaction and thermal fluctuations are expected to have similar effects as in metallic systems.